We introduce a fast algorithm for parameter estimation in multidimensional Hawkes processes, a widely used class of temporal point processes for mutually exciting discrete event data. Our approach assumes a low-rank structure on the infectivity parameter of the multidimensional Hawkes process, and relies on a method of moments estimator. Notably, it requires only a single scan of the data, and consistently recovers an accurate representation of the underlying graph structure, while sidestepping numerical stability issues inherent in Hawkes process estimation. Finally, we make connections between our method and spectral clustering, and observe that our contributions result in natural methods for clustering temporal point processes. Our algorithm can be used for community detection and graph cluster discovery in large networks of asynchronous event streams such as high-dimensional neural spike trains, log streams of large computer networks, or high-frequency financial data. We present favorable empirical results on synthetic data, and an application to clustering currency pairs via high-frequency price jumps.

中文翻译：

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使用低等级 Hawkes 进程对事件流进行聚类

我们在多维霍克斯过程中引入了一种用于参数估计的快速算法，这是一种广泛使用的时间点过程，用于相互激发的离散事件数据。我们的方法假设多维霍克斯过程的传染性参数的低秩结构，并依赖于矩估计方法。值得注意的是，它只需要对数据进行一次扫描，并始终如一地恢复底层图结构的准确表示，同时回避了霍克斯过程估计中固有的数值稳定性问题。最后，我们将我们的方法和谱聚类联系起来，并观察到我们的贡献导致了聚类时间点过程的自然方法。我们的算法可用于大型异步事件流网络中的社区检测和图集群发现，例如高维神经尖峰序列、大型计算机网络的日志流或高频金融数据。我们提出了关于合成数据的有利实证结果，以及通过高频价格上涨来聚类货币对的应用。